Abstract
The effective method basing on theory of R-functions and variational structural method is developed for solving of non-linear boundary problems. Elastic-plastic bending of thin shallow shells is considered. The problems are reduced to finding of stationar points of suggested mixed variational functionals according to initial linearization by use of schemes of subsequent loading and Newton-Kantorovich jointly with method of varying elastic parameters. The method is used for automatic calculations in POLE programming system for calculations of shell structural elements. The numerical justification of the method is given. New laws of non-linear deformation of shallow shells and plates with complex shape in plane are established.
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